Hello TristanBX,
Welcome to Apple Support Communities. It sounds like you're having trouble with videos not playing on your iPhone. We are happy to share information that may help.
In order to isolate this issue, you may want to try a different network, whether that be by trying a different Wi-Fi network or using cellular data. If it happens with both Wi-Fi and cellular data, be sure to check for any available updates for your iPhone: Update your iPhone, iPad, or iPod touch. You'll want to have a current backup prior to updating.
If this is happening while connected to cellular data, check for a carrier settings update: Update your carrier settings on your iPhone or iPad.
If this is only occurring while using Wi-Fi, try resetting your network settings. Here are the steps: tap Settings > General > Reset > Reset Network Settings. This also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you’ve used before.
Take care.